An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later,…

The present study aimed to investigate the effects of geometry instruction activities conducted in nature based on modeling, game-based, and cooperative learning methods on achievement, mathematical motivation, and visual mathematical literacy perceptions of third-grade elementary school students. The present study is a quantitative study…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…

This study focuses on assessing the contribution of ELL services to Spanish-speaking students' mathematics learning in elementary schools. ELL students tend to have lower average math achievement at school entry and throughout elementary school. The term "ELL services" encompasses English-as-a-second-language (ESL) programs, bilingual…

Teaching experiments with pairs of children have generated several hypotheses about students' construction of fractions. For example, Steffe (2004) hypothesized that robust conceptions of improper fractions depends on the development of a splitting operation. Results from teaching experiments that rely on scheme theory and Steffe's hierarchy of…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

This study aimed to evaluate the impact of individual differences in working memory capacity on number transcoding. A recently proposed model, ADAPT (a developmental asemantic procedural transcoding model), accounts for the development of number transcoding from verbal form to Arabic form by two mechanisms: the learning of new production rules…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

Notes that Montessori classrooms provide children with the opportunity to explore and discover mathematics. Describes the introduction to Pascal's Triangle as a suggested opportunity to connect young children to deep mathematical truths. Provides teachers with materials requirements, and notes ideas on what can be acquired from the problem, the…